1. The problem statement, all variables and given/known data The right angle boom which supports the 230-kg cylinder is supported by three cables and a ball-and-socket joint at O attached to the vertical x-y surface. Determine the reactions at O and the cable tensions. 2. Relevant equations M = r x F unit vector = (vector)/(magnitude of vector) weight = weight of hanging mass = 230*9.81 = 2256.3 N 3. The attempt at a solution So far, I've gotten two of the reaction forces and two of the cable tensions. Using unit vectors, I was able to solve for the tension vectors: T_ac = <-.4745, .4745, -.7414>T_ac T_bd = <0, .7880, -.6156>T_bd T_be = <0, 0, -1>T_be Because the moment about an axis sums to zero: ΣM_x = 0 0 = (weight of mass - .4745*T_ac - .7880*T_bd)*radius from axis T_ac = (1/.4745)(2256.3 - .7880*T_bd) ΣM_z = 0 0 = (T_bd*.7880 - .5*weight)*radius from axis T_bd = 1431.66 N which goes to 1430 N (The homework site I'm using only allows three significant digits.) T_ac = (1/.4745)(2256.3 - .7880*T_bd) T_ac = 2377.56 N which goes to 2380 N Up until this point, all the forces were equidistant from the axis in question. Somewhere in here my numbers get messed up - the previous two tension forces are correct, but this one is wrong. ΣM_y = 0 0 = T_ac*-.4745*2.5 - T_be*-1*1.9 - T_be*1.9 + .6156*1.9*T_bd T_be = (1/1.9)(T_ac*.4745*2.5 - .6156*1.9*T_bd) T_be = 606 N Solving for the reaction forces: ΣF_x = 0 0 = T_ac*-.4745 + O_x O_x = 1130 N ΣF_y = 0 0 = O_y + .4745*T_ac + T_bd*.7880 - weight O_y = 0 N These two reaction forces are correct, so if I'm doing something wrong up to this point, I'm making compensating errors. The next reaction force is incorrect, but it depends on T_be and since I know that number is wrong, even if my method here is correct, I won't be able to get the right answer. ΣF_z = 0 0 = -.7414*T_ac - .6156*T_bd - T_be + O_z O_z = 3250 N I'm not sure what I'm doing wrong, but at this point I'd be happy to find any mistake! Thanks for your time!